Civil Engineering Reference
In-Depth Information
Figure 2.36
Bending moment diagram, curvature distribution and plastic hinge length in a cantilever column
estimated from the likely curvature distributions. The ductility of a frame member depends on the
spreading of inelasticity, which takes place in the region corresponding to the plastic hinge of length
L
p
in Figure 2.36. Longitudinal steel bars elongate beyond the base of the cantilever member given in
Figure 2.36 because of the fi nite bond stress. This elongation causes additional rotation and defl ection
in the member; this response is referred to as yield penetration. Additionally, interactions between
fl exural - and shear -induced cracks increase the spreading of plasticity in the critical region.
Plastic hinges should be located in beams rather than in columns since the columns are responsible
for the gravity load resistance, hence the stability of the structure against collapse. Shear capacity of
both beams and columns should always be higher than fl exural strength to avoid brittle shear failure.
To ensure adequate rotational ductility (e.g.
μ
θ
≥ 10 - 15) in fl exural plastic hinges, it is necessary to
carefully detail critical regions (plastic hinges). For example, in RC members, it is essential to provide
closely spaced stirrups, which confi ne effectively the concrete and use suffi cient lap splices and anchor-
age lengths. For steel and composite members, cross sections employing plates with low width-to-
thickness ratios in plastic hinge regions are necessary in order to avoid local buckling.
(iv) Connection Properties
The behaviour of connections (e.g. beam- to - column in MRFs, brace - to - column and brace - to - beam in
either CBFs or EBFs, and those between superstructure and foundation systems) affects signifi cantly
the global ductile response of structures. In RC frames, the ductile behaviour of joints is a function of
several design parameters, which include, among others: (i) joint dimension, (ii) amount of steel rein-
forcement, (iii) bond resistance, (iv) level of column axial loads, and (v) presence of slab and transverse
beams framing into the connection. All other parameters being equal, by increasing joint dimensions
lower shear stresses are generated. The advantage of increasing column depths is twofold. Joint shear
stresses are considerably reduced and bond demands on longitudinal steel reinforcement of beam bars
passing through the joint are minimized. Both effects prevent brittle failure modes in RC beam-to-
column joints, i.e. loss of bond resistance along the joint boundary, inability to resist high stresses
caused by perimeter bond actions and inability to sustain diagonal compression strut in the joint core.
Brittle failure due to low shear capacity can be prevented by adequately confi ning the joint by hoops.
In so doing, shear strength and bond resistance are enhanced. Occurrence of bond failure endangers
the ductile behaviour of frames and should be prevented when designing RC joints. Similarly, the pres-
ence of slabs may erode the ductility of beam-to-column connections because of the additional shear
demand caused by the raised beam moment. Effects of column axial loads reduce the total lateral drift
